How Can I make a Fluid Simulation liquid become gooey or viscous?
Primarily you want to adjust the viscosity settings. The smaller the viscosity the more watery the simulation. Note that the exponent value is negated so increasing the exponent makes the final value smaller.

You will also find that the real world size makes a difference. A real world size of 10.0 will give a watery result while a real world size of 0.2 will be closer to a slushy with the same viscosity.

As for twisting the result, it will depend on the effect you want. You could use a simple deform modifier or a lattice deform. With a thick fluid sim you may also be able to use a collision object that spins around.